Initially left on the bench by Solskjaer, his introduction seven minutes before the break drew a huge cheer from the crowd and he repaid their faith with a game-changing performance.
Darting in from the left, he slipped a perfect through-ball to Craig Bellamy, who became the first player to score for seven different Premier league clubs as he cancelled out Robert Snodgrass's opener with a low finish.
"It was a decision I had to make there and then," added Solskjaer. "I was hoping we'd be in a better position, but I felt we needed some spark, and that's what we got from Zaha."
Less than two minutes later, Kenwyne Jones marked his debut with a goal, firing home from close-range at the second attempt after his initial header was blocked.
Cardiff were indebted to their goalkeeper David Marshall, who produced a string of superb saves to deny Norwich, who also struck the woodwork twice and had two goals disallowed for offside.
Cardiff had a bit of luck - Solskjaer
Solskjaer admitted his team had ridden their luck to come away with their first win in eight league games and his first victory in the league after three defeats.
"Before now, we've had some very good performances but no luck," said Solskjaer. "Maybe the fair result would have been a draw if you look at possession and shots, but we got a result with a little bit of luck."
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